### Educational Resource: Understanding Probability Distributions **Problem 641: Analysis of Intern Monthly Pay Distribution** 1. **Context**: Based on data from a Glassdoor source, the mean monthly pay for interns at Facebook is $6,898. 2. **Statistical Assumptions**: Assume the intern monthly pay is normally distributed with a standard deviation of $500. 3. **Questions to Consider**: - **a. Probability of Pay Less Than $5,900?** - **b. Probability of Pay Between $5,700 and $6,100?** - **c. Probability of Pay Above $6,500?** - **d. What percentage of intern monthly pays are higher than $6,100?** - **e. Ninety-five percent of the intern monthly pays are between what two values, symmetrically distributed around the mean?** - **f. Compare the results for these intern pays to those computed in Problem 640.** ### Detailed Explanation - **Normal Distribution**: A probability distribution where data is symmetrically distributed around the mean. In this problem, it helps us estimate probabilities of various salary ranges using the given mean and standard deviation. - **Use of Z-Scores**: To solve the questions, one would typically convert salary values into Z-scores to find probabilities from a standard normal distribution table. - **Interpreting the Results**: For instance, by calculating Z-scores, you could determine the percentage of interns earning below or above certain thresholds and the specific range encompassing 95% of the salaries. This problem assists students in applying statistical concepts such as normal distribution, standard deviation, and Z-scores to real-world salary data, providing a practical understanding of these mathematical ideas.
### Educational Resource: Understanding Probability Distributions **Problem 641: Analysis of Intern Monthly Pay Distribution** 1. **Context**: Based on data from a Glassdoor source, the mean monthly pay for interns at Facebook is $6,898. 2. **Statistical Assumptions**: Assume the intern monthly pay is normally distributed with a standard deviation of $500. 3. **Questions to Consider**: - **a. Probability of Pay Less Than $5,900?** - **b. Probability of Pay Between $5,700 and $6,100?** - **c. Probability of Pay Above $6,500?** - **d. What percentage of intern monthly pays are higher than $6,100?** - **e. Ninety-five percent of the intern monthly pays are between what two values, symmetrically distributed around the mean?** - **f. Compare the results for these intern pays to those computed in Problem 640.** ### Detailed Explanation - **Normal Distribution**: A probability distribution where data is symmetrically distributed around the mean. In this problem, it helps us estimate probabilities of various salary ranges using the given mean and standard deviation. - **Use of Z-Scores**: To solve the questions, one would typically convert salary values into Z-scores to find probabilities from a standard normal distribution table. - **Interpreting the Results**: For instance, by calculating Z-scores, you could determine the percentage of interns earning below or above certain thresholds and the specific range encompassing 95% of the salaries. This problem assists students in applying statistical concepts such as normal distribution, standard deviation, and Z-scores to real-world salary data, providing a practical understanding of these mathematical ideas.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Educational Resource: Understanding Probability Distributions
**Problem 641: Analysis of Intern Monthly Pay Distribution**
1. **Context**: Based on data from a Glassdoor source, the mean monthly pay for interns at Facebook is $6,898.
2. **Statistical Assumptions**: Assume the intern monthly pay is normally distributed with a standard deviation of $500.
3. **Questions to Consider**:
- **a. Probability of Pay Less Than $5,900?**
- **b. Probability of Pay Between $5,700 and $6,100?**
- **c. Probability of Pay Above $6,500?**
- **d. What percentage of intern monthly pays are higher than $6,100?**
- **e. Ninety-five percent of the intern monthly pays are between what two values, symmetrically distributed around the mean?**
- **f. Compare the results for these intern pays to those computed in Problem 640.**
### Detailed Explanation
- **Normal Distribution**: A probability distribution where data is symmetrically distributed around the mean. In this problem, it helps us estimate probabilities of various salary ranges using the given mean and standard deviation.
- **Use of Z-Scores**: To solve the questions, one would typically convert salary values into Z-scores to find probabilities from a standard normal distribution table.
- **Interpreting the Results**: For instance, by calculating Z-scores, you could determine the percentage of interns earning below or above certain thresholds and the specific range encompassing 95% of the salaries.
This problem assists students in applying statistical concepts such as normal distribution, standard deviation, and Z-scores to real-world salary data, providing a practical understanding of these mathematical ideas.
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6.41.
Let X be the monthly pay of an intern at Facebook.
From the given information, X follows normal distribution with mean µ=$6,589 and a standard deviation σ=$500.
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